Comparison of 2D and 3D density-weighted displacement speed statistics and implications for laser based measurements of flame displacement speed using direct numerical simulation data
Comparison of 2D and 3D density-weighted displacement speed statistics and implications for laser based measurements of flame displacement speed using direct numerical simulation data
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DOI：
10.1016/j.combustflame.2010.11.014
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发表时间：
2011-07
影响因子：
4.4
通讯作者：
N. Chakraborty;G. Hartung;M. Katragadda;C. Kaminski
中科院分区：
文献类型：
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作者：
N. Chakraborty;G. Hartung;M. Katragadda;C. Kaminski
在最近的研究中，已经提出了光片成像方法（Hartung等人，J. Appl. Phys. B 96（2009）843-862），其允许测量量Sd = 2D，其是湍流预混火焰的实际密度加权位移速度Sd = 2D的二维投影。在这里，统计的Sd和Sd 2Dare比较使用的统计平面湍流预混火焰的直接数值模拟数据库。结果表明，在湍流速度脉动u′的均方根值较小的情况下，Sd <$2D的概率密度函数（pdfs）与Sd <$2D的概率密度函数（pdfs）具有较好的近似性，尽管Sd <$2D的pdfs比Sd <$2D的pdfs宽.尽管Sd <$2D和Sd <$2D的pdfs与标准差之间的一致性随着u′的增加而变差，但在这里考虑的所有情况下，Sd <$2D的平均值与Sd <$2D的平均值密切对应。发现二维曲率κ m2 D和密度加权位移速度St 2Dare的二维切向扩散分量的pdf比它们的三维对应物（即分别为κ和St）窄。发现π/2×κ m ~ 2D和π/2×St ~ 2D的pdfs、平均值和标准差分别忠实地反映了相应三维对应物κ和St ~ 2D的pdfs、平均值和标准差。与Sd * pdf相比更宽的Sd * 2Dpdf和与St * pdf相比更窄的St * 2Dpdf的组合，导致比密度加权位移速度Sr *+Sn * 的组合反应和正扩散分量的pdf更宽的[公式：见文本] pdf。这反映在[公式：见正文]的标准偏差值高于其三维对应物Sr +Sn的标准偏差值。然而，[公式：见正文]的平均值仍然接近Sr +Sn的平均值。二维和三维量之间的完美相关性的丧失导致[公式：见正文]和Sr +Sn-κm之间以及Sd 2D-κ m2 D和Sd-κ m之间的重要定性差异。对于单位刘易斯数火焰，Sd ε-κ m关联仍然是强负的，而Sd ε 2D和κ m 2D之间观察到弱关联。该研究表明，密度加权位移速度的测量，这是重要的详细的模型开发或实验数据的基础上验证的背景下，平面成像技术的预测能力的优势和局限性。
In a recent study, a light sheet imaging approach has been proposed (Hartung et al., J. Appl. Phys. B 96 (2009) 843–862) which permits measurement of a quantity Sd∗2D, which is the two-dimensional projection of the actual density-weighted displacement speed Sd∗for turbulent premixed flames. Here the statistics of Sd∗and Sd∗2Dare compared using a direct numerical simulation database of statistically planar turbulent premixed flames. It is found that the probability density functions (pdfs) of Sd∗2Dapproximate the pdfs of Sd∗satisfactorily for small values of root-mean-square turbulent velocity fluctuation u′, though the Sd∗2Dpdfs are wider than the Sd∗pdfs. Although the agreement between the pdfs and the standard-deviations of Sd∗2Dand Sd∗deteriorate with increasing u′, the mean values of Sd∗2Dcorrespond closely with the mean values of Sd∗for all cases considered here. The pdfs of two-dimensional curvature κm2Dand the two-dimensional tangential-diffusion component of density-weighted displacement speed St∗2Dare found to be narrower than their three-dimensional counterparts (i.e. κmand St∗respectively). It has been found that the pdfs, mean and standard-deviation of π/2×κm2Dand π/2×St∗2Dfaithfully capture the pdfs, mean and standard-deviation of the corresponding three-dimensional counterparts, κmand St∗respectively. The combination of wider Sd∗2Dpdfs in comparison to Sd∗pdfs, and narrower St∗2Dpdfs in comparison to St∗pdfs, leads to wider [Formula: see text] pdfs than the pdfs of combined reaction and normal-diffusion components of density-weighted displacement speed Sr∗+Sn∗. This is reflected in the higher value of standard-deviation of [Formula: see text] , than that of its three-dimensional counterpart Sr∗+Sn∗. However, the mean values of [Formula: see text] remain close to the mean values of Sr∗+Sn∗. The loss of perfect correlation between two and three-dimensional quantities leads to important qualitative differences between the [Formula: see text] and Sr∗+Sn∗-κm, and between the Sd∗2D-κm2Dand Sd∗-κmcorrelations. For unity Lewis number flames, the Sd∗-κmcorrelation remains strongly negative, whereas a weak correlation is observed between Sd∗2Dand κm2D. The study demonstrates the strengths and limitations of the predictive capabilities of the planar imaging techniques in the context of the measurement of density-weighted displacement speed, which are important for detailed model development or validation based on experimental data.